Project Phoenix was the code name for an operation undertaken at least in part by Section 31.
As part of the project, Section 31 retrieved the body of USS Enterprise and USS Enterprise-A Captain James T. Kirk from Veridian III sometime after his re-emergence and death in 2371 for the purposes of the project. Kirk's body was stored aboard Daystrom Station, a high-security black site of the Daystrom Institute, as of 2401. (PIC: "The Bounty")
This project was only mentioned in writing.